Problem: Simplify the following expression: $\sqrt{40}-\sqrt{160}+\sqrt{90}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{40}-\sqrt{160}+\sqrt{90}$ $= \sqrt{4 \cdot 10}-\sqrt{16 \cdot 10}+\sqrt{9 \cdot 10}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{10}-\sqrt{16} \cdot \sqrt{10}+\sqrt{9} \cdot \sqrt{10}$ $= 2\sqrt{10}-4\sqrt{10}+3\sqrt{10}$ Finally, simplify by combining the terms. $= ( 2 - 4 + 3 )\sqrt{10} = \sqrt{10}$